The notion of stability also exists in this setting. As in the smi case, a matching \(M\)  is stable if there is no pair of agents who would rather be assigned to each other than to their assigned partners in \(M\)  (if any).
Using a counterexample, [1]} showed that a stable matching in sr need not exist in all instances. [2]} gave an \(O(n^2)\)  algorithm to find a stable matching in sr or report that no such matching exists.
